Have an answer to each box to correctly complete the derivation of a formula for the area of a sector of a circle.
Suppose a sector of a circle with radius r has a central angle of θ
. Since a sector is a fraction of a __________ circle, the ratio of a sector's area A to the circle's area is equal to the ratio of the central angle to the measure of a full rotation of the circle. A full rotation of a circle is 2π radians. This proportion can be written as A/πr2=_____________ Multiply both sides by πr2 and simplify to get ________, where θ is the measure of the central angle of the sector and r is the radius of the circle.
Please help guys, you rock! I am not very good at proofs haha
The stuff in red goes into each respective blank
Note, werty.....that the second blank can be interpreted like this :
A / [ pi r^2 ] = θ / [ 2pi ] [ multiply both sides by pi r^2 ]
A = [ θ / 2 ] r^2 = (1/2)r^2 θ